The maximum or minimum number of rational points on curves of genus three over finite fields

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dc.creatorLauter, Kristin
dc.creatorSerre, Jean-Pierre
dc.date2001-04-07
dc.date.accessioned2026-07-25T23:11:51Z
dc.descriptionWe show that for all finite fields F_q, there exists a curve C over F_q of genus 3 such that the number of rational points on C is within 3 of the Serre-Weil upper or lower bound. For some q, we also obtain improvements on the upper bound for the number of rational points on a genus 3 curve over F_q.
dc.description28 pages including the appendix. Main paper by Kristin Lauter, appendix by Jean-Pierre Serre
dc.identifierhttps://arxiv.org/abs/math/0104086
dc.identifierhttp://arxiv.org/abs/math/0104086
dc.identifierCompositio Mathematica 134 (p. 87-111) 2002
dc.identifier.urihttps://dspace.dare.co.zw/handle/123456789/96353
dc.subjectAlgebraic Geometry
dc.subjectNumber Theory
dc.subject14G45 (Primary) 11G10, 14K15, 11D45 (Secondary)
dc.titleThe maximum or minimum number of rational points on curves of genus three over finite fields
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